The ecological pyramid of number represents the number of individuals at each trophic level in an ecosystem. In this case, we have:
(a) (i) Describe the population growth curve applicable in a population of any species in nature that has limited resources at its disposal.
(ii) Give the equation of this growth curve.
(iii) Name the growth curve and depict a graphical plot for this type of population growth.
OR
(b) (i) Explain the Species-Area relationship within a natural forest and also predict the nature of the graph when species richness is plotted against the area for a wide variety of taxa.
(ii) Depict the graphical relationship between species richness and area.
(iii) Give the equation of the Species-Area relationship for a wide variety of taxa on a logarithmic scale.
(a) (i) Describe the population growth curve applicable in a population of any species in nature that has unlimited resources at its disposal.
(ii) Explain the equation of this growth curve.
(iii) Name the growth curve and depict a graphical plot for this type of population growth.
OR
(b) (i) Explain the conclusion drawn by Alexander von Humboldt during his extensive explorations in the wilderness of South American jungles.
(ii) Give the equation of the Species-Area relationship.
(iii) Draw a graphical representation of the relation between species richness and area for a wide variety of taxa such as birds, bats, etc.
In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is applied, electrons move with an average velocity known as drift velocity (vd). The average time between successive collisions is known as relaxation time (τ ). The magnitude of drift velocity per unit electric field is called mobility (μ). An expression for current through the conductor can be obtained in terms of drift velocity, number of electrons per unit volume (n), electronic charge (−e), and the cross-sectional area (A) of the conductor. This expression leads to an expression between current density (-j) and the electric field (E→ ). Hence, an expression for resistivity (ρ) of a metal is obtained. This expression helps us to understand increase in resistivity of a metal with increase in its temperature, in terms of change in the relaxation time (τ ) and change in the number density of electrons (n).
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction 90° is called the critical angle (ic) for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of lens, ’lensemaker formula’ is obtained.